A man enter the doors of the "WeWork" co-operative co-working space on March 13, 2013 in Washington, DC. Photo: Getty Images

It’s an idea factory.

As the city’s tech sector explodes, one Manhattan building is a hotbed for new inventions — including robot-controlled ovens, cellphone alcohol testers, and even “smart diapers.”

WeWork’s communal office on Broadway and Fulton Street has 900 startups across eight floors. It has free beer all day, an arcade, ping-pong, and scores of entrepreneurs in glass-sided suites.

“Our members are bringing things into existence every day, so we consider ourselves the community for creators,” said WeWork co-founder Adam Neumann, who now runs 10 other locations citywide, all inspired by his upbringing in a kibbutz.

One firm, PreciBake, is turning ovens into artificial-intelligence machines. The system’s sensors fit inside existing ovens to control the temperature and detect whether a batch is too crisp or inconsistent with a shop’s recipe.

On the same floor, in a tiny glass office, Alcohoot is turning smartphones into police-grade breath-alcohol testers. The $119 mouthpiece plugs into the headphone jack and tracks drinkers’ blood-alcohol levels and displays whether they are legally intoxicated.

Co-founder Ben Biron, who served in Israel’s military, said he created Alcohoot to combat drunken driving after learning many soldiers were dying in alcohol-related wrecks.

Meanwhile, Pixie Scientific’s husband-and-wife team, Yaroslav Faybishenko and Jennie Rubinshteyn, are developing a “smart diaper” for children and adults alike. The garment has built-in test strips that detect signs of urinary-tract infections, Type 1 diabetes and other illnesses.

At Kinsa, founder Inder Singh is creating a $24 thermometer that takes temps while plugged into smartphones. Eventually users’ data will anonymously make up a world map, so symptoms can be tracked by geographic region or even school district.

Singh said the thermometers will advance his mission to “create a real-time map of human health to stop the spread of disease globally.”

Other startups include Booze Carriage, an online alcohol-delivery service that’s similar to Seamless, and Sexual Health Innovations, which runs a Web site that allows people to send their partners anonymous notifications on STDs.

But not all of WeWork’s members are ultra high-tech. Care and Wear, which rents a $450-a-month desk inside the building’s “lab,” is set to release a fashionable armband for cancer patients that covers the long, thin tubes used for chemotherapy.

Last week, a report by state Comptroller Thomas DiNapoli revealed New York’s tech industry is growing four times faster than the rest of the city’s economy.